Background

This document has nls (non-linear least squares) regression fits using the log-normal functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. stand age relationships. This functional form is commonly used in growth analyses, and permits a flexible shape to fit to data in an intermediate maximum (i.e., “hump” shaped) relationship. We use the sum of tree biomass growth increment method for the plot biomass growth (\(G\)) calculation (see supplementary methods). Models are fitted separately by US ecoprovince.

Hypothetically, the entire functional form of the following non-linear model is considered: \(G = (1 + (yr-1990) \cdot ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(StdAge_{t1}\) is the FIA-estimated stand age at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(G\), \(c\): the \(StdAge_{t1}\) value at peak \(G\), and \(d\): the curve shape parameter.

Data have increasing variance in \(G\) with increasing \(StdAge_{t1}\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}\) in equal-sample sized plot biomass bins (n=20) for each ecoprovince.

Model selection is used to determine. to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:

model 1: simple model \(G = (1 + (yr-1990) \cdot ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

model 2: phi model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

model 3: phi-alpha model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

NOTE:

This document contains all \(G\) observations that meet our plot based filtering criteria:

exclude FIA plots in plantation forests
exclude FIA plots with multiple plot conditions (COND_PROG_UNADJ > 0.95)
exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):

case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)

These data set cleaning criteria resulted in the exclusion of 1677 observations.

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   6799     5243.9                                
## 2   6798     5240.3  1   3.547   4.6014 0.03198 *  
## 3   6797     4946.6  1 293.714 403.5836 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25284.27
## 2     2 25281.66
## 3     3 24891.20

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.292872   0.163470   1.792   0.0732 .  
## phi    0.010286   0.004348   2.366   0.0180 *  
## alpha  0.644419   0.030041  21.451   <2e-16 ***
## a     -6.319123  16.323713  -0.387   0.6987    
## b      9.731894  16.313339   0.597   0.5508    
## c     29.516194   1.963439  15.033   <2e-16 ***
## d      4.920382   4.450084   1.106   0.2689    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8531 on 6797 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 7.621e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1  18726      16075                                  
## 2  18721      16009  5   66.26   15.498 3.029e-15 ***
## 3  18720      14917  1 1091.78 1370.124 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 65771.72
## 2     2 65686.39
## 3     3 64365.59

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.885982   0.141057   6.281 3.44e-10 ***
## phi    0.025852   0.002867   9.018  < 2e-16 ***
## alpha  0.827263   0.020518  40.319  < 2e-16 ***
## a      0.722858   0.373130   1.937   0.0527 .  
## b      1.832104   0.365116   5.018 5.27e-07 ***
## c     19.734593   0.815916  24.187  < 2e-16 ***
## d      2.337867   0.345363   6.769 1.33e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8927 on 18720 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.592e-06
##   (48 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 23 rows containing missing values (geom_point).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_221$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_221.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Error in nls(fg2_1, data = G_222, start = c(ge = ge.start, a = a.start,  : 
##   singular gradient

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_222$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_222.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   8769     9241.0                                 
## 2   8768     9226.3  1  14.662  13.933 0.0001906 ***
## 3   8764     9007.0  4 219.303  53.346 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 35056.50
## 2     2 35044.56
## 3     3 34826.34

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.129281   0.098622 -11.451  < 2e-16 ***
## phi   -0.022440   0.005652  -3.970 7.25e-05 ***
## alpha  0.584152   0.038447  15.194  < 2e-16 ***
## a      2.669375   0.482960   5.527 3.35e-08 ***
## b      1.970422   0.471662   4.178 2.97e-05 ***
## c     29.057795   1.872699  15.517  < 2e-16 ***
## d      1.426937   0.289803   4.924 8.64e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.014 on 8764 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.379e-06
##   (12 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 5 rows containing missing values (geom_point).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1  12311      21643                              
## 2  12310      21640  1    2.8    1.591 0.2072    
## 3  12309      19118  1 2522.2 1623.870 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 60187.33
## 2     2 60187.74
## 3     3 58663.54

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -0.0986057  0.0991469  -0.995    0.320    
## phi    0.0007941  0.0040244   0.197    0.844    
## alpha  0.8567398  0.0191847  44.658   <2e-16 ***
## a      3.2349735  0.2112777  15.311   <2e-16 ***
## b      3.2164895  0.1944758  16.539   <2e-16 ***
## c     18.2273027  0.4124116  44.197   <2e-16 ***
## d      1.3141944  0.0855111  15.369   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.246 on 12309 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 6.922e-06
##   (31 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 14 rows containing missing values (geom_point).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq   F value    Pr(>F)    
## 1  12395      26336                                   
## 2  12394      26317  1   18.36    8.6448  0.003286 ** 
## 3  12393      23747  1 2570.16 1341.3010 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 61358.26
## 2     2 61351.61
## 3     3 60079.33

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.006466   0.122537   0.053   0.9579    
## phi    0.008872   0.004511   1.967   0.0493 *  
## alpha  0.842963   0.020444  41.232   <2e-16 ***
## a      3.481881   0.118222  29.452   <2e-16 ***
## b      2.594932   0.109338  23.733   <2e-16 ***
## c     16.557370   0.402833  41.102   <2e-16 ***
## d      0.923104   0.049522  18.640   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.384 on 12393 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.51e-06
##   (70 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 29 rows containing missing values (geom_point).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   1255     2849.6                             
## 2   1254     2849.5  1   0.12  0.0529 0.8181    
## 3   1253     2692.6  1 156.84 72.9850 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6292.826
## 2     2 6294.773
## 3     3 6225.438

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.870346   0.901176   0.966 0.334336    
## phi   -0.009029   0.021670  -0.417 0.677010    
## alpha  0.784819   0.082801   9.478  < 2e-16 ***
## a      3.281058   0.556974   5.891 4.93e-09 ***
## b      1.518118   0.413630   3.670 0.000253 ***
## c     18.156020   2.676847   6.783 1.81e-11 ***
## d      0.782773   0.244040   3.208 0.001373 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.466 on 1253 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 8.926e-06
##   (5 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits ## plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96816, p-value = 5.09e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.1636, p-value = 0.001558
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 3 rows containing missing values (geom_point).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in nls(fg2_2, data = G_242, start = c(ge = ge.start, phi = phi.start,  : 
##   singular gradient
## Error in nls(fg2_3, data = G_242, start = c(ge = ge.start, phi = phi.start,  : 
##   singular gradient
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1784     1637.6                                 
## 2   1783     1633.2  1  4.3616  4.7617   0.02923 *  
## 3   1782     1617.6  1 15.6039 17.1896 3.542e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6743.615
## 2     2 6740.844
## 3     3 6725.669

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.54768    0.29899  -1.832   0.0671 .  
## phi    0.02158    0.01084   1.992   0.0466 *  
## alpha  0.40164    0.09302   4.318 1.66e-05 ***
## a     -0.12904    5.50243  -0.023   0.9813    
## b      3.43455    5.50316   0.624   0.5326    
## c     29.00246    6.18140   4.692 2.91e-06 ***
## d      3.46196    3.40815   1.016   0.3099    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9528 on 1782 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 6.493e-06
##   (8 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93225, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.924, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Error in nls(fg2_1, data = G_263, start = c(ge = ge.start, a = a.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(fg2_2, data = G_263, start = c(ge = ge.start, phi = phi.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(fg2_3, data = G_263, start = c(ge = ge.start, phi = phi.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_263$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_263.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_315.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

## Error in nls(fg2_1, data = G_322, start = c(ge = ge.start, a = a.start,  : 
##   missing or negative weights not allowed
## Error in nls(fg2_2, data = G_322, start = c(ge = ge.start, phi = phi.start,  : 
##   missing or negative weights not allowed
## Error in nls(fg2_3, data = G_322, start = c(ge = ge.start, phi = phi.start,  : 
##   missing or negative weights not allowed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_322.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6722     4631.1                                
## 2   6721     4611.3  1  19.79  28.851  8.08e-08 ***
## 3   6720     4290.0  1 321.32 503.331 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24157.98
## 2     2 24131.16
## 3     3 23647.28

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.839969   0.191442   4.388 1.16e-05 ***
## phi    0.017844   0.004027   4.431 9.53e-06 ***
## alpha  0.638474   0.026475  24.116  < 2e-16 ***
## a      2.450566   0.125126  19.585  < 2e-16 ***
## b      0.708020   0.082579   8.574  < 2e-16 ***
## c     27.878887   1.761763  15.824  < 2e-16 ***
## d      0.942137   0.155951   6.041 1.61e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.799 on 6720 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 5.478e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   8028      11387                              
## 2   8027      11381  1   6.68   4.7111   0.03 *  
## 3   8026      11111  1 269.82 194.9038 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 36089.85
## 2     2 36087.14
## 3     3 35896.40

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.408200   0.127552  -3.200  0.00138 ** 
## phi   -0.009929   0.005572  -1.782  0.07478 .  
## alpha  0.726136   0.049523  14.663  < 2e-16 ***
## a      3.204776   0.316637  10.121  < 2e-16 ***
## b      1.983587   0.276232   7.181 7.55e-13 ***
## c     26.015032   1.721337  15.113  < 2e-16 ***
## d      1.219745   0.203133   6.005 2.00e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.177 on 8026 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.777e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model     AIC
## 1     1 3510.88
## 2     2      NA
## 3     3      NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge   2.4228     1.2810   1.891  0.05892 .  
## a    1.5037     0.2854   5.268 1.73e-07 ***
## b    1.0411     0.3042   3.422  0.00065 ***
## c   25.8961     2.6460   9.787  < 2e-16 ***
## d    0.5208     0.1315   3.961 8.08e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.126 on 877 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 7.76e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98047, p-value = 1.762e-09
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.1975, p-value = 0.2311
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Error in nls(fg2_1, data = G_M231, start = c(ge = ge.start, a = a.start,  : 
##   number of iterations exceeded maximum of 50

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_M231$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M231.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   3138     7449.1                             
## 2   3137     7446.7  1   2.39  1.0065 0.3158    
## 3   3132     7043.5  5 403.23 35.8603 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 15644.22
## 2     2 15645.21
## 3     3 15457.14

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.091782   0.342038  -3.192  0.00143 ** 
## phi   -0.004369   0.015974  -0.274  0.78446    
## alpha  0.997556   0.068924  14.473  < 2e-16 ***
## a      4.878930   0.466285  10.463  < 2e-16 ***
## b      3.462861   0.526379   6.579 5.54e-11 ***
## c     33.740147   1.345010  25.085  < 2e-16 ***
## d      0.412764   0.049270   8.378  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.5 on 3132 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.439e-06
##   (40 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95864, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.648, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (geom_point).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value    Pr(>F)    
## 1   1939     3672.5                                 
## 2   1938     3467.6  1 204.88 114.5044 < 2.2e-16 ***
## 3   1929     3346.6  9 121.07   7.7541 2.764e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8948.829
## 2     2 8839.235
## 3     3 8742.612

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.52119    0.30445  -4.997 6.36e-07 ***
## phi    0.18344    0.01370  13.394  < 2e-16 ***
## alpha  0.76789    0.08709   8.817  < 2e-16 ***
## a      3.08729    1.55632   1.984  0.04743 *  
## b      4.49689    1.54267   2.915  0.00360 ** 
## c     35.53892    7.53152   4.719 2.54e-06 ***
## d      1.93337    0.66181   2.921  0.00353 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.317 on 1929 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 2.342e-06
##   (27 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96034, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.6402, p-value = 0.008286
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 6 rows containing missing values (geom_point).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_M313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M313.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_M331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M331.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)    
## 1   2604     2857.0                               
## 2   2603     2850.5  1   6.585  6.0134 0.01426 *  
## 3   2594     2650.2  9 200.295 21.7833 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9021.477
## 2     2 9017.457
## 3     3 8812.761

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.65586    0.47035  -1.394  0.16331    
## phi    0.03633    0.01614   2.251  0.02447 *  
## alpha  0.84555    0.05293  15.975  < 2e-16 ***
## a      0.68227    0.94027   0.726  0.46814    
## b      2.02084    0.96660   2.091  0.03665 *  
## c     56.12184    4.44187  12.635  < 2e-16 ***
## d      2.01474    0.67929   2.966  0.00304 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.011 on 2594 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.49e-06
##   (48 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88013, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.8595, p-value = 6.912e-12
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 12 rows containing missing values (geom_point).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Error in nls(fg2_1, data = G_M333, start = c(ge = ge.start, a = a.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_M333$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M333.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in nls(fg2_3, data = G_M334, start = c(ge = ge.start, phi = phi.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_M334$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M334.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

Fitted parameters

Best / selected models by ecoprovince

Code	Ecoregion	Sel.Mod
211	Northeastern Mixed Forest	3
212	Laurentian Mixed Forest	3
221	Eastern Broadleaf Forest	NA
222	Midwest Broadleaf Forest	NA
223	Central Interior Broadleaf Forest	3
231	Southeastern Mixed Forest	3
232	Outer Coastal Plain Mixed Forest	3
234	Lower Mississippi Riverine Forest	3
242	Pacific Lowland Mixed Forest	NA
251	Prairie Parkland (Temperate)	3
255	Prairie Parkland (Subtropical)	NA
261	California Coastal Chaparral Forest and Shrub	NA
262	California Dry Steppe	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	NA
313	Colorado Plateau Semi-Desert	NA
315	Southwest Plateau and Plains Dry Steppe and Shrub	NA
321	Chihuahuan Semi-Desert	NA
322	American Semidesert and Desert	NA
331	Great Plains/Palouse Dry Steppe	NA
332	Great Plains Steppe	NA
341	Intermountain Semi-Desert and Desert	NA
342	Intermountain Semi-Desert	NA
411	Everglades	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	3
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	3
M223	Ozark Broadleaf Forest Meadow	1
M231	Ouachita Mixed Forest	NA
M242	Cascade Mixed Forest	3
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	3
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	NA
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	NA
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	3
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	NA
M334	Black Hills Coniferous Forest	NA
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	NA

table by ecoprovince

Code	Ecoregion	region	n.obs	n.plots	ge	ge.2.5	ge.97.5	phi	phi.2.5	phi.97.5	alpha	alpha.2.5	alpha.97.5	a	a.2.5	a.97.5	b	b.2.5	b.97.5	c	c.2.5	c.97.5	d	d.2.5	d.97.5
211	Northeastern Mixed Forest	east	6806	2847	0.2928722	-0.0275809	0.6133253	0.0102855	0.0017619	0.0188092	0.6444186	0.5855286	0.7033086	-6.3191225	-38.3187109	25.680466	9.7318944	-22.2473568	41.7111455	29.51619	25.66724	33.36515	4.9203821	-3.8031757	13.6439400
212	Laurentian Mixed Forest	east	18775	8891	0.8859822	0.6094972	1.1624673	0.0258523	0.0202335	0.0314711	0.8272635	0.7870466	0.8674804	0.7228585	-0.0085100	1.454227	1.8321037	1.1164438	2.5477637	19.73459	18.13532	21.33386	2.3378675	1.6609244	3.0148105
221	Eastern Broadleaf Forest	east	7170	3490	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
222	Midwest Broadleaf Forest	east	4877	2401	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
223	Central Interior Broadleaf Forest	east	8783	3725	-1.1292810	-1.3226030	-0.9359591	-0.0224402	-0.0335203	-0.0113600	0.5841517	0.5087863	0.6595171	2.6693754	1.7226598	3.616091	1.9704217	1.0458534	2.8949900	29.05780	25.38686	32.72873	1.4269371	0.8588555	1.9950187
231	Southeastern Mixed Forest	east	12347	5691	-0.0986057	-0.2929491	0.0957377	0.0007941	-0.0070943	0.0086826	0.8567398	0.8191348	0.8943448	3.2349735	2.8208361	3.649111	3.2164895	2.8352865	3.5976925	18.22730	17.41891	19.03569	1.3141944	1.1465794	1.4818095
232	Outer Coastal Plain Mixed Forest	east	12470	6101	0.0064662	-0.2337262	0.2466585	0.0088722	0.0000291	0.0177152	0.8429634	0.8028894	0.8830374	3.4818813	3.2501488	3.713614	2.5949315	2.3806130	2.8092501	16.55737	15.76776	17.34698	0.9231039	0.8260340	1.0201738
234	Lower Mississippi Riverine Forest	east	1265	714	0.8703464	-0.8976346	2.6383273	-0.0090288	-0.0515430	0.0334854	0.7848195	0.6223761	0.9472628	3.2810584	2.1883541	4.373763	1.5181181	0.7066343	2.3296020	18.15602	12.90442	23.40762	0.7827729	0.3040002	1.2615457
242	Pacific Lowland Mixed Forest	pacific	81	81	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
251	Prairie Parkland (Temperate)	east	1797	809	-0.5476846	-1.1340860	0.0387169	0.0215844	0.0003274	0.0428414	0.4016421	0.2191965	0.5840877	-0.1290406	-10.9209373	10.662856	3.4345485	-7.3587801	14.2278772	29.00246	16.87890	41.12601	3.4619597	-3.2224364	10.1463557
255	Prairie Parkland (Subtropical)	pacific	663	293	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
261	California Coastal Chaparral Forest and Shrub	pacific	24	24	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
262	California Dry Steppe	pacific	0	0	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	pacific	155	155	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
313	Colorado Plateau Semi-Desert	interior west	215	215	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
315	Southwest Plateau and Plains Dry Steppe and Shrub	interior west	4	4	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
321	Chihuahuan Semi-Desert	interior west	9	9	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
322	American Semidesert and Desert	interior west	3	3	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
331	Great Plains/Palouse Dry Steppe	interior west	304	240	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
332	Great Plains Steppe	interior west	195	106	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
341	Intermountain Semi-Desert and Desert	interior west	62	62	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
342	Intermountain Semi-Desert	interior west	121	120	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
411	Everglades	east	93	61	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	east	6729	2989	0.8399694	0.4646825	1.2152563	0.0178435	0.0099492	0.0257379	0.6384745	0.5865748	0.6903741	2.4505658	2.2052783	2.695853	0.7080204	0.5461401	0.8699006	27.87889	24.42527	31.33250	0.9421365	0.6364232	1.2478498
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	east	8034	3700	-0.4082001	-0.6582347	-0.1581655	-0.0099293	-0.0208518	0.0009931	0.7261363	0.6290585	0.8232142	3.2047759	2.5840854	3.825466	1.9835873	1.4421005	2.5250742	26.01503	22.64076	29.38930	1.2197454	0.8215529	1.6179378
M223	Ozark Broadleaf Forest Meadow	east	883	343	2.4227544	-0.0915226	4.9370314	NA	NA	NA	NA	NA	NA	1.5037012	0.9435126	2.063890	1.0411436	0.4440579	1.6382293	25.89607	20.70279	31.08934	0.5208208	0.2627350	0.7789067
M231	Ouachita Mixed Forest	east	988	481	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M242	Cascade Mixed Forest	pacific	3179	3176	-1.0917823	-1.7624233	-0.4211414	-0.0043693	-0.0356894	0.0269508	0.9975558	0.8624148	1.1326968	4.8789296	3.9646741	5.793185	3.4628610	2.4307789	4.4949430	33.74015	31.10296	36.37734	0.4127636	0.3161582	0.5093689
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	pacific	1963	1963	-1.5211913	-2.1182783	-0.9241044	0.1834450	0.1565842	0.2103058	0.7678897	0.5970888	0.9386907	3.0872948	0.0350396	6.139550	4.4968882	1.4714163	7.5223600	35.53892	20.76815	50.30968	1.9333652	0.6354259	3.2313045
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	interior west	19	19	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	362	362	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	1711	1711	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	2649	2648	-0.6558624	-1.5781636	0.2664388	0.0363264	0.0046821	0.0679706	0.8455463	0.7417608	0.9493318	0.6822728	-1.1614916	2.526037	2.0208352	0.1254576	3.9162128	56.12184	47.41187	64.83181	2.0147404	0.6827438	3.3467371
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	1675	1675	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M334	Black Hills Coniferous Forest	interior west	362	170	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	interior west	213	213	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map2

## Warning: package 'ggnewscale' was built under R version 4.2.1

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 23 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 23 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 1 rows containing missing values (geom_hline).

## Warning: Removed 23 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 23 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US -0.03960663
## 2       pacific -1.13380170
## 3          east  0.14185716
## 4 interior west -0.22981654

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US  0.012690540
## 2       pacific  0.060826694
## 3          east  0.006197611
## 4 interior west  0.012728892

alpha (biomass growth compensation effect)

##          region weighted.alpha
## 1     entire US      0.6087266
## 2       pacific      0.8214344
## 3          east      0.6359597
## 4 interior west      0.2962825

Calculations - weighted averages subsetted to 15 ecoprovinces

ecoprovince codes: 211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332

ge

##          region weighted.ge
## 1     entire US  -0.0462044
## 2       pacific  -1.2558084
## 3          east   0.1506365
## 4 interior west  -0.6558624

phi

##          region weighted.phi
## 1     entire US  0.014804563
## 2       pacific  0.067372162
## 3          east  0.006581174
## 4 interior west  0.036326372

alpha

##          region weighted.alpha
## 1     entire US      0.7101298
## 2       pacific      0.9098277
## 3          east      0.6753185
## 4 interior west      0.8455463

FIA - NLS Models: Biomass Growth vs. Stand Age

JAH

2022-10-25

Background

211 - Northeastern Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

summary

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

summary

plot residuals

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

summary

plot residuals

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

plot residuals

predict and plot

plotting 2

262 - California Dry Steppe

model selection 1

summary

plot residuals

predict and plot